The hole i assume is the rear end fill hole for when you add the drive fluid for the rear end. Just a threaded plug is what should be in the hole. I wouldnt run with out the plug because debris and can get inside and wreak havoc on the internal gears.

That is a "vent tube" and "gear lube filler hole" part#jn3-47559-00-00. (all the same from 1979 to 1994,if you want to find a good used one) and it should be there to stop things getting like mentioned. Original G1-a's had the choke cable mounted on the instimment panel next to the key switch, your's has been modified, Yamaha no longer sell's the choke cable, you'll have to go aftermarket for that, if you want it stock.